Contractive presentations: A family of inverse monoids and semigroups with finiteR-classes

There has recently been considerable interest in inverse monoids which are presented by generators and relations. In this work the author employs graphical techniques to investigate the word problem for presentations of inverse monoids which generalize the case in which all relations in a presentation are of the formw=w ² . The work also investigates free objects in finitely based varieties of inverse semigroups, where the free objects have similar presentations. A fundamental charecteristic of the monoids (semigroups) investigated is: ifF is a free inverse monoid andM=F/θ, then form∈F, theR-class ofmθ has no more elements than theR-class ofm.